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from manimlib.imports import *
class parametricHelix(ThreeDScene, GraphScene):
def construct(self):
self.x_min = -5
self.y_min = -4
self.graph_origin = ORIGIN
self.x_max = 5
self.y_max = 4
self.x_axis_label = ""
self.y_axis_label = ""
self.x_axis_width = 10
self.y_axis_height = 7.5
ax1 = ThreeDAxes().scale(0.65).shift(2.6*RIGHT+DOWN+np.array([0,0,0.5]))
axes_group = []
self.setup_axes()
self.axes.shift(3*RIGHT + 2*UP).scale(0.3)
axes_group.append(self.axes)
self.setup_axes()
self.axes.shift(3*RIGHT + 2*DOWN).scale(0.3)
axes_group.append(self.axes)
axes_group = VGroup(*axes_group)
asint_text = TextMobject(r'$x = a\sin{t}$').scale(0.7).shift(4*RIGHT + 3*UP)
xlabel1 = TextMobject(r'$x$').shift(3.3*RIGHT + 3.7*UP).scale(0.7)
tlabel1 = TextMobject(r'$t$').shift(5*RIGHT + 2*UP).scale(0.7)
up_text = VGroup(*[asint_text, xlabel1, tlabel1])
asint = ParametricFunction(
lambda t: np.array([
t,
np.sin(t),
0
]), t_min = -4*np.pi, t_max = 4*np.pi, color = GREEN_E
).shift(3*RIGHT + 2*UP).scale(0.12)
acost_text = TextMobject(r'$y = a\cos{t}$').scale(0.7).shift(4*RIGHT + DOWN)
ylabel1 = TextMobject(r'$y$').shift(3.3*RIGHT+0.3*DOWN).scale(0.7)
tlabel2 = TextMobject(r'$t$').shift(5*RIGHT + 2*DOWN).scale(0.7)
down_text = VGroup(*[acost_text, ylabel1, tlabel2])
acost = ParametricFunction(
lambda t: np.array([
t,
np.cos(t),
0
]), t_min = -4*np.pi, t_max = 4*np.pi, color = BLUE
).shift(3*RIGHT + 2*DOWN).scale(0.12)
up_dot = Dot(color = RED).scale(0.6)
down_dot = Dot(color = RED).scale(0.6)
helix_dot = Dot(radius = 0.16, color = RED)
zlabel = TextMobject(r'$z$').scale(0.7).shift(3*UP + 2.8*LEFT)
ylabel2 = TextMobject(r'$y$').scale(0.7).shift(0.3*DOWN+0.15*RIGHT)
xlabel2 = TextMobject(r'$x$').scale(0.7).shift(0.5*DOWN + 6.4*LEFT)
helix_text = TextMobject(r'$x = a\sin{t}$ \\ $y = a\cos{t}$ \\ $z = ct$').scale(0.7).shift(2.3*UP + 1.3*LEFT)
main_text = VGroup(*[xlabel2, ylabel2, zlabel, helix_text])
helix = ParametricFunction(
lambda t: np.array([
np.cos(TAU*t),
np.sin(TAU*t),
0.4*t
]), t_min = -2*np.pi/3, t_max = 1.8*np.pi/3, color = WHITE
).shift(ax1.get_center())
self.set_camera_orientation(phi = 75*DEGREES, theta=45*DEGREES)
t_tracker = ValueTracker(-12.56)
t=t_tracker.get_value
t_label = TexMobject(
"t = ",color=WHITE
).next_to(helix_text,DOWN, buff=0.2).scale(0.6)
t_text = always_redraw(
lambda: DecimalNumber(
t(),
color=WHITE,
).next_to(t_label, RIGHT, buff=0.2)
).scale(0.6)
group = VGroup(t_text,t_label).scale(1.5).move_to(ORIGIN).shift(2*DOWN)
self.add_fixed_in_frame_mobjects(axes_group, main_text, up_text, down_text, acost, asint)
self.play(FadeIn(ax1), FadeIn(axes_group), FadeIn(asint), FadeIn(acost), FadeIn(helix), FadeIn(up_text), FadeIn(down_text), FadeIn(main_text))
#self.begin_ambient_camera_rotation(rate = 0.06)
self.add_fixed_in_frame_mobjects(up_dot, down_dot, group)
self.play(MoveAlongPath(up_dot, asint, run_time = 8), MoveAlongPath(down_dot, acost, run_time = 8), MoveAlongPath(helix_dot, helix, run_time = 8), t_tracker.set_value,12.56, rate_func=linear, run_time=8)
self.play(FadeOut(VGroup(*[ax1, axes_group, asint, acost, helix, up_text, down_text, main_text, up_dot, down_dot, helix_dot, group])))
self.wait(1)
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